A 3-dimensional absolute retract which does not contain any disk
A 3-dimensional irreducible compact absolute retract which contains no disc
A Bing-Borsuk retract which contains a 2-dimensional absolute retract [Book]
A boundary set for the Hilbert cube containing no arcs
A characterization of MAR and MANR-spaces by extendability of mutations
A characterization of regular averaging operators and its consequences
We present a characterization of continuous surjections, between compact metric spaces, admitting a regular averaging operator. Among its consequences, concrete continuous surjections from the Cantor set 𝓒 to [0,1] admitting regular averaging operators are exhibited. Moreover we show that the set of this type of continuous surjections from 𝓒 to [0,1] is dense in the supremum norm in the set of all continuous surjections. The non-metrizable case is also investigated. As a consequence, we obtain...
A class α and locally connected continua which can be ε-mapped onto a surface
A construction of noncontractible simply connected cell-like two-dimensional Peano continua
Using the topologist sine curve we present a new functorial construction of cone-like spaces, starting in the category of all path-connected topological spaces with a base point and continuous maps, and ending in the subcategory of all simply connected spaces. If one starts from a noncontractible n-dimensional Peano continuum for any n > 0, then our construction yields a simply connected noncontractible (n + 1)-dimensional cell-like Peano continuum. In particular, starting from the circle 𝕊¹,...
A generalization of cohomotopy groups
A Lefschetz-type fixed point theorem
A locally connected non-movable continuum that fails to separate
A note on singularities in ANR's
A note on topological m-spaces
A remark on Fox's paper on shape
A remark on the retracting of a ball onto a sphere in an infinite dimensional Hilbert space.
A survey of various modifications of the notions of absolute retracts and absolute neighborhood retracts
A theory of absolute proper retracts
A theory of proper shape for locally compact metric spaces
AANR spaces and absolute retracts for tree-like continua
Continua that are approximative absolute neighborhood retracts (AANR’s) are characterized as absolute terminal retracts, i.e., retracts of continua in which they are embedded as terminal subcontinua. This implies that any AANR continuum has a dense arc component, and that any ANR continuum is an absolute terminal retract. It is proved that each absolute retract for any of the classes of: tree-like continua, -dendroids, dendroids, arc-like continua and arc-like -dendroids is an approximative absolute...
Absolute fixed-point sets in compacta